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Finding the Third Proportional to 31,977 and 48,412

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Solution

The third proportional to 31,977 and 48,412 is: 73,293.98

Step by Step Solution

  1. Step 1: Write the proportion equation
    31,977 : 48,412 = 48,412 : x
  2. Step 2: Convert to fraction form
    31,977/48,412 = 48,412/x
  3. Step 3: Cross multiply
    31,977x = 48,412 × 48,412
  4. Step 4: Simplify right side
    31,977x = 2,343,721,744
  5. Step 5: Solve for x
    x = 2,343,721,744/31,977
  6. Step 6: Final answer
    x = 73,293.98

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Why These Related Problems?

These problems maintain the same ratio (1.51) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.